Question

Катер прошел 12 км против течения реки и 5 км по течению. при этом он затратил столько времени сколько ему потребовалось бы , если бы он шел 18 км по озеру. какова собственная скорость катера, если известно, что скорость течения реки равна з км/час ?

Answer 1

Х км/ч скорость катера. по течению х+3км  а против течения х-3км . по озеру  скорость х а расстояние 18х км.теперь составляем уравнение. 12/х-3 + 5/х+3=18/х теперь осталось решить это уравнение. найденный х это и есть скорость катера-6-не удовлетворяет уловию задачиОтвет:27 километров в час. х - собств.скор.катерах+3 - скор по теч. х-3 - скор пр.теч 18/х - время по озеру Уравнение: 12/(x-3)+5/(x+3)=18/x Преобразуется в квадратное: x^2-21*x-162=0 x1=27 (км/ч) x2=-6 
Воот

Answer 2

Problem Analysis

We are given that a boat traveled 12 km against the current of a river and then 5 km with the current. The boat took the same amount of time as it would have taken to travel 18 km on a lake. We need to find the boat's speed.

Solution

Let's assume the boat's speed is x km/h and the speed of the river's current is z km/h.

When the boat is traveling against the current, its effective speed is reduced by the speed of the current. So, the boat's speed against the current is (x - z) km/h.

When the boat is traveling with the current, its effective speed is increased by the speed of the current. So, the boat's speed with the current is (x + z) km/h.

We can use the formula distance = speed × time to calculate the time taken for each leg of the journey.

For the first leg of the journey (against the current), the boat traveled 12 km. So, the time taken is 12 / (x - z) hours.

For the second leg of the journey (with the current), the boat traveled 5 km. So, the time taken is 5 / (x + z) hours.

According to the problem, these two times are equal to the time it would have taken to travel 18 km on a lake. So, we can set up the equation:

12 / (x - z) = 5 / (x + z) = 18 / x

To solve this equation, we can cross-multiply and simplify:

12(x + z) = 5(x - z)

12x + 12z = 5x - 5z

7x = -17z

x = -17z / 7

Therefore, the boat's speed is -17z / 7 km/h.

Answer

The boat's speed is -17z / 7 km/h, where z is the speed of the river's current in km/h.